8.2 Multidimensional Finite Difference Kalman Filters

8.2.1 Multidimensional Finite Difference State Prediction

In manner similar to the approach taken in the one-dimensional case, we first repeat the multidimensional state prediction equation developed for the EKF given by (7.33)

(8.26) equation

Now, using the second-order finite difference term of multidimensional Stirling's polynomial given by equation (2.74) and letting xc and x0 = 0, (8.26) becomes

(8.27) equation

where ej is a unit vector along the Cartesian axis of the j th dimension and q is a step size that must be finite, real, and greater than zero.

Defining

(8.28) equation

leads to the identities

(8.29) equation

and

(8.30) equation

Here, img is a free parameter that determines the value of q. To maintain q as finite, real, and greater than zero, we must restrict img to the ...

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